Fast verification of solutions of matrix equations

Shin'Ichi Oishi, Siegfried M. Rump*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


In this paper, we are concerned with a matrix equation Ax = b where A is an n × n real matrix and x and b are n-vectors. Assume that an approximate solution x is given together with an approximate LU decomposition. We will present fast algorithms for proving nonsingularity of A and for calculating rigorous error bounds for ∥A-1 b - x̃∥. The emphasis is on rigour of the bounds. The purpose of this paper is to propose different algorithms, the fastest with 2/3n3 flops computational cost for the verification step, the same as for the LU decomposition. The presented algorithms exclusively use library routines for LU decomposition and for all other matrix and vector operations.

Original languageEnglish
Pages (from-to)755-773
Number of pages19
JournalNumerische Mathematik
Issue number4
Publication statusPublished - 2002 Feb 1

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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